Resonance in NMR

A big question in NMR is "what is actually happening when a sample is pulsed with Rf?" The technique is called Nuclear Magnetic Resonance because the nuclei seem to resonate with the incoming radiofrequency pulse, but what does "resonate" mean?

• Are photons of Rf absorbed by nuclei, which changes the spin state to a higher state? The photons are then re-emitted when the spin state returns to normal?
• Is it an elastic collision? Where a photon hits the nucleus, boosts the spin to a higher state, then bounces away? If this was true, the energy aka frequency of the photon should change since it transferred energy to change the spin state of the nucleus, but it does not.
• If the nuclear spin is thought of as a wave, then does the wave of the incoming photon temporarily modulate the wave of the nuclear spin in the same way modulation of radio works? So after bouncing around the nucleus a few times the photon wave leaves again.